What is the value of f(4+h)-f(4)/h?

f(x) = 2x²-5x+2

f(4) = 2×4² - 5×4 + 2
= 32 - 20 + 2
= 14

f(4+h)
= 2(4+h)² - 5(4+h) + 2
= 2(16+8h+h²) - 20 - 5h + 2
= 32+16h+2h²-20-5h+2
= 2h²+11h+14


(f(4+h)-f(4))/h
= 2h+11


As h→0
(f(4+h)-f(4))/h → 11

If you are familiar with derivatives note that f'(4)=11

f(x)=[2(4+h)^2-5(4+h)+2-2(4^2)+5(4)-2]/h
=[2(16+8h+(h^2))-20-5h+2-2(16)+5(4)-2]/h
=[32+16h+2(h^2)-20-5h+2-32+20-2]/h
=[16h+2(h^2)-5h]/h
=[h(11+2h)]/h
=11+2h=11 (if you are doing the lim as h approaches 0)

i think you want to find the value of [f(4+h)-f(4)]/h
if it is,
sol:
as f(x)=2x^2-5x+2.
at first,
f(4+h)=2(4+h)^2-5(4+h)+2 [by replacing x with 4+h]
=2(16+h^2+8h)-20-5h+2
=32+2h^2+16h-5h-18
=2h^2+11h+14
f(4+h)=2h^2+11h+14


f(4)=2(4)^2-5(4)+2 [by replacing x with 4]
=2*16-20+2
=32-18
=14
f(4)=14


therefore,
[f(4+h)-f(4)]/h
=(2h^2+11h+14-14)/h
=(2h^2+11h)/h
=h(2h+11)/h [by taking h common from numerator]
=2h+11

I think ur question is wrong. It might be
[f(4+h) - f(4)] / h
If so,
f(x) = 2x^2 – 5x + 2

f(4+h) = 2(4+h)^2 – 5(4+h) + 2
= 2(16 + 8h + h^2) – 20 – 5h + 2
= 32 + 16h + 2h^2 – 18 – 5h
= 14 + 11h + 2h^2
f(4+h)= 2h^2 + 11h + 14

f(4) = 2(4)^2 – 5(4) + 2
= 2(16) – 20 + 2
= 32 – 18
=14
f(4) = 14

f(4+h) – f(4) = 2h^2 + 11h + 14 – 14
f(4+h) – f(4) = 2h^2 + 11h

[f(4+h) – f(4)] / h = (2h^2 + 11h) / h
= 2h + 11

Thus, [f(4+h) – f(4)] / h = 2h + 11

Or if ur question is f(4+h) - f(4)/h, then,
f(4+h)= 2h^2 + 11h + 14
f(4)= 14
So, f(4)/h = 14h^(-1)
Thus, f(4+h) – f(4)/ h = 2h^2 + 11h + 14 – 14h^(-1)

f(x) = 2x^2 - 5x + 2
f(x + h) = 2(x + h)^2 - 5(x + h) + 2
f(x + h) = 2(x + h)(x + h) - 5*x - 5*h + 2
f(x + h) = 2(x^2 + 2xh + h^2) - 5x - 5h + 2
f(x + h) = 2x^2 + 4xh + 2h^2 - 5x - 5h + 2

[f(x + h) - f(x)]/h
= [2x^2 + 4xh + 2h^2 - 5x - 5h + 2 - (2x^2 - 5x + 2)]/h
= [2x^2 + 4xh + 2h^2 - 5x - 5h + 2 - 2x^2 + 5x - 2]/h
= [2x^2 - 2x^2 + 2h^2 + 4xh - 5x + 5x - 5h + 2 - 2]/h
= [2h^2 + 4xh - 5h]/h

[f(4 + h) - f(4)]/h
= [2h^2 + 4(4)h - 5h]/h
= [2h^2 + 16h - 5h]/h
= 2h + 16 - 5
= 2h + 11

first of all my friend i think that you wrote it wrong..i think is find the value of (f(4+h)-f(4))/h.that is seems better-))
so:f(4+h)=2(4+h)^2 -5(4+h) +2(substituting (4+h) in the place of x)
=2h^2 +16h +32 -20 - 5h +2=2h^2 +11h +14
and:f(4)=2(4)^2-5(4)+2(substituting 4 in the place of x)
=32 - 20 + 2 =14
hence (f(4+h)-f(4))/h=(2h^2 + 11h +14- 14)/h=(2h^2 + 16h)/h=h(2h + 11)/h
=2h +11
i hope so that i helped-))